Download Astronomy 104: Stellar Astronomy

Astronomy 104:
Stellar Astronomy
Lecture 5: Observing is the key ...
Brahe and Kepler
Spring Semester 2013
Dr. Matt Craig
1
For next time:
•Read Slater and Freedman 3-5 and 3-6 if
you haven't already.
•Focus on 3-6 on Gravity
•We will touch on topics in 3-5 as well!
•Maybe look at the Study Guide for Quiz
#1 scheduled for Tue., Sept. 18.
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Objectives (all in 3-4)
•Understand Kepler’s 3 Laws of Planetary Motion.
•Understand the Consequences of the First Law.
•Identify the shape of the orbit of a planet.
•Understand the Consequences of the Second Law.
•Deduce how much of its time an object spends on each part of its
orbit.
•Predict how fast a star or planet moves in each part of its orbit.
•[Next time] Understand the Consequences of the Third
Law.
•Compare the periods of two planets given their distances from the
Sun.
•Compare the distance to the Sun of two planets given their periods.
•Describe the effect a planet's mass has on its orbital speed.
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Clicker Question
•Why is a scientific theory supposed to
predict, and not just explain after the fact?
(A)The scientific method is supposed to be
followed in order.
(B) People can usually think up explanations
after something happens, but they may not
be right.
(C) Predicting things before they happen
requires more understanding – you are more
likely to have the correct explanation.
(D)Both (B) and (C)
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Kepler breaks a Paradigm
•Paradigm: A worldview
underlying the theories and
methodology of a particular
scientific subject.
•Medieval Paradigm: Planetary
orbits are circular.
•Example of a Paradigm Shift:
Kepler realizes planetary orbits
are not circular ... quickly
Kepler reduces the entire
problem of determining the
positions of planets (any
anything orbiting the Sun) to
three simple laws!
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Tycho Brahe:
The Bad Boy of Astronomy
•Made very accurate
observations
•Didn’t think heliocentric
model was right since no
parallax of stars observed.
Tycho Brahe (1546-1601 CE)
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Tycho’s Life’s Work
•Major contribution – a
substantial increase in
accuracy in positions of
stars and planets
•10x more precise than
anyone before
(previously planetary
positions had only
been measured to ±10
arcminutes).
•Reached limit
achievable with human
vision (accurate to 1-2
arcminutes)
The Mural Quadrant (from Tycho’s 1598
Astronomiae Instauratae Mechanica).
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Johannes Kepler
•Tycho’s assistant
(until Tycho died)
•Used Tycho’s
observations to find a
model more accurate
than Ptolemy or
Copernicus
Johannes Kepler
(1571 – 1630 CE)
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Kepler’s Three Laws:
1.Planetary orbits are ellipses with the Sun at
one Focus.
2.Planets sweep out equal area of their orbits
in equal time.
3.A planet’s orbital period, P, is related to its
semi-major axis distance from the Sun, a, by
the relationship P2 = ka3
(where k is constant).
•Note: Kepler had no idea why his laws were
correct!
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Ptolemy vs Kepler
•Ptolemy
•Kepler
•8 different complicated
•3 laws
laws-one each for:
•Apply to any
•Stars
object in orbit.
•Sun
•All planets
•Moon
•Moons of Jupiter
•Mercury
•Satellites orbiting
•Venus
Earth
•Mars
•Every other
orbiting system
•Jupiter
ever seen!
•Saturn
Kepler’s 1st Law:
•Planetary orbits are ellipses with the Sun at one
Focus [ORBIT SHOWN BELOW IS A COMET,
NOT A PLANET]
•What is an ellipse?
All points where the sum of
the distances from the two foci is 2a.
Useful Relationship:
Semi-major axis (a) is
half the major axis. It is
also equal to the
average distance of a
planet from the Sun.
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Clicker Question
•Which of the shapes below do you think
most closely matches the shape of the
orbit of a typical planet?
A.
B.
C.
D. None of the above
Almost Circular Orbits
•Hard to to
see “noncircularness”
in shape of
orbit...
•Easier to see
in position of
Sun.
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A Very Useful Difference
•Kepler’s
Laws work
for
anything
orbiting
the Sun...
not just
planets.
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Clicker Question
Which of the shapes below most
closely matches the shape of the
orbit of a typical planet?
A
B
Sun is not at the center
C
Kepler’s Second Law
•Sounds complicated:
•Planets sweep out equal area of their orbits in
equal time.
•Has a simple to describe physical effect,
and a fairly simple explanation.
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Lecture Tutorial--Kepler’s Second Law
•“Kepler’s Second Law” on pages 13-16 of
Lecture-Tutorials Book.
•Remember:
•work in groups of 2 to 4.
•come to consensus about the answer to each
question before you write down your answer.
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Clicker Question
Kepler&s Second Law 1 Instructor&s Guide
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ADDITIONAL QUESTIONS
•Refer to the diagram in answering the question
The planet in the orbit shown in
the drawing at right obeys
Kepler6s Laws. Use this drawing
to answer the next four questions.
below:
4
B
3
5
2
1. According to Kepler6s Second
A
C
1
Law, during which one of the
6
portion of the planets orbit GBI,
GCI, or GDI, would the planet
7
D 8
take the same amount of time
as it took for the portion of the
orbit identified with letter GAI? If you think all the portions of the orbit take the same amount
of time, answer GEI. [B is the correct answer]
•According to Kepler’s Second Law, during
2. During which part of the planet6s orbit (A, B, C, or D) would the planet move with the
greatest speed? [C is the correct answer]
which one of the portions of the planet’s orbit
“B”, “C”, or “D”, would the planet take the
same amount of time as it took for the portion
of the orbit identified with letter “A”? If you
think all the portions of the orbit take the same
amount of time, answer “E”.
3. During how many portions of the planet6s orbit (A, B, C and D) would the planet be speeding
up the entire time?
a.
b.
c.
d.
e.
Only during one of the portions shown.
During two of the portions shown.
During three of the portions shown.
During four of the portions shown.
None of the above.
4. During which of the portions of the planet6s orbit would the planet experience an increase in
speed for at least a moment?
a. Only during one of the portions shown.
b. During two of the portions shown.
c. During three of the portions shown.
d. During four of the portions shown.
e. None of the above.
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Clicker Question
Kepler&s Second Law 1 Instructor&s Guide
31
•Refer to the diagram in answering the
ADDITIONAL QUESTIONS
question below:
The planet in the orbit shown in
the drawing at right obeys
Kepler6s Laws. Use this drawing
to answer the next four questions.
4
B
3
5
2
1. According to Kepler6s Second
A
C
1
Law, during which one of the
6
portion of the planets orbit GBI,
GCI, or GDI, would the planet
7
D 8
take the same amount of time
as it took for the portion of the
orbit identified with letter GAI? If you think all the portions of the orbit take the same amount
of time, answer GEI. [B is the correct answer]
•During which part of the planet’s orbit
2. During which part of the planet6s orbit (A, B, C, or D) would the planet move with the
greatest speed? [C is the correct answer]
(“A”, “B”, “C”, or “D”) would the planet
move with the greatest speed? If you think
it moves at the same speed in all parts,
answer “E” instead.
3. During how many portions of the planet6s orbit (A, B, C and D) would the planet be speeding
up the entire time?
a.
b.
c.
d.
e.
Only during one of the portions shown.
During two of the portions shown.
During three of the portions shown.
During four of the portions shown.
None of the above.
4. During which of the portions of the planet6s orbit would the planet experience an increase in
speed for at least a moment?
a. Only during one of the portions shown.
b. During two of the portions shown.
c. During three of the portions shown.
d. During four of the portions shown.
e. None of the above.
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Clicker Question
•Kepler’s 2nd Law tells us what about the
motion of one object orbiting another?
A) The orbit of one object around another is
elliptical.
B) As the objects get closer together, they move
faster in their orbits.
C) As the object approaches the star, it slows down.
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Kepler’s Laws Elsewhere
•Kepler’s Laws apply to
any object orbiting any
other object.
Including ...
• binary stars (two stars
orbiting each other).
•stars orbiting the black hole at the center
of the Galaxy.
•Galaxies orbiting other galaxies.
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Binary Stars and Kepler’s Laws
•The orbit of each
star is indeed an
ellipse.
•Each star follows
its own 2nd law,
sweeping out
equal areas in
equal time.
• The stars do
indeed speed up as
they approach
each other and
slow down as they
separate.
Images from http://astrosun2.astro.cornell.edu/academics/courses/astro201/kepler_binary.htm
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For next time:
•Read Slater and Freedman 3-5 and 3-6 if
you haven't already.
•Focus on 3-6 on Gravity
•We will touch on topics in 3-5 as well!
•Maybe look at the Study Guide for
Midterm #1 scheduled for Tue., Feb.5.
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